settings.outformat = "pdf";
unitsize(1cm);
fill((0, 0){up}..(1, 1)..(2, sqrt(2))--(2, 0)-- cycle, mediumgray);
draw((-.1, 0)--(2, 0), arrow = Arrow(TeXHead));
draw((0, -.1)--(0, 2), arrow = Arrow(TeXHead));
draw((0, 0){up}..(1, 1)..(2, sqrt(2)));